2016/09/19 by Aline Marguet, Marguet, Aline · 1 citation
Mathematics · Medicine · #COVID-19 epidemiological studies #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1609.05678
openalex publication_date 2016/09/19 · arxiv created 2018/11/19 · arxiv updated 2018/11/20 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of the descendants at birth depends on the trait of the mother and on the number of descendants. In this article, we explicitly describe the penalized Markov process, named auxiliary process, corresponding to the dynamic of the trait along the spine by giving its associated infinitesimal generator. We prove a Many-to-One formula and a Many-to-One formula for forks. Furthermore, we prove that this auxiliary process characterizes exactly the process of the trait of a uniformly sampled individual in the large population approximation. We detail three examples of growth-fragmentation models: the linear growth model, the exponential growth model and the parasite infection model.